Backing to arbor - arbor knot
Fly line to backing - nail knot
Butt section (10-12") to fly line - nail knot
Leader to butt section - loop to loop connection via the double surgeons loop (faster to tie than the perfection loop and, unlike the perfection loop, it creates a loop in line with the standing line)
Tippet to leader - double surgeons knot

If you don't like nail knots just bear with it. After all, they'll be the only two you have to tie unless you get new lines. The loop to loop connection is fast strong and prevents the butt section from being shorted and lost from nail or blood knotting your leaders.